I betcha don’t remember that he does that, but there is one point where, if you think back, I’m sure you’ll remember it. It’s when you light all the torches in the bottom floor of Goron City, which makes the giant clay pot spin around, for some reason. And then, also for some reason, Link spins too. Why?
Skawo, one of the best Youtubers I’ve found for getting to the bottom of mysteries like this, did a sixteen-minute video explaining it.
Here is a brief text explanation. Some cutscenes are programmed so that Link turns to face the subject of the scene, a given actor in it, presumably to make it look more realistic. This is a little clumsily done though. The “location” of the actor, its location in 3D space, is usually near its feet (it being the most relevant location for collision checks), so actors have a second location, for cutscene-Link to stare at.
There’s even a special process for this, to make Link’s turning seem more natural: his head turns first, then the rest of his body. But, who knows why, during the clay pot cutscene, Link’s focus point is himself. The focus point is connected to his body, and the angle is a little off-center, he turns his head to look at it, his body rotates beneath it, causing the focus point to move, and so continue the rotation.
This, by itself, is pretty minor. But more than that, the focus point is also a bit above Link’s head, so he looks up at the same time. Eventually, the focus point rotates so far around that it’s technically behind Link, and that makes the horizontal rotation angle nearly 180 degrees, increasing the rate of spin considerably.
This isn’t the whole story, just a tl;dw. In fact, it’s just half of it, which then moves over to a different cutscene, one from the 3DS version of the game. For more, please refer to Skwaro’s video above.